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Equilibrium and Center of Mass. In Fig. 13-11, a horizontal scaffold, of length 2.00 m and uniform mass 50 kg, is suspended from a building by two cables. It has dozens of paint cans stacked on it at various points. The total mass of the paint cans is 77.0 kg. The tension in the cable at the right is 735 N.
Assuming the mass of an object acts at a point allows us to calculate how objects will respond to different forces. It is sometimes referred to as the centre of gravity. Finding the centre of mass for a regularly shaped object with a uniform density is easy, it can be done by drawing. If you have an irregular shaped or non-symmetrical object ...
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Using a single integral we were able to compute the center of mass for a one-dimensional object with variable density, and a two dimensional object with constant density. With a double integral we can handle two dimensions and variable density.
This is a uniform object, so the center of mass is in the center of the object, in this case the middle of the hula hoop. No actual material except air is present at that spot, so it is not possible to put the support directly under the center of mass.
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2 Uniform Objects Uniform Objects C of M is located in the center of the object C of M is located in the center of the object CALCULATING THE POSITION OF THE Because the center of gravity depends on distance and mass from the pivot point, objects with large masses count more heavily.
The center of mass of a uniform solid triangle lies on all three medians and therefore at the centroid, which is also the average of the three vertices. An experimental method for locating the center of mass is to suspend the object from two locations and to drop plumb lines from the suspension points.